Abstract root subgroups and quadratic action. With an Appendix by A. E. Zalesskii

DOI10.1006/aima.1998.1779zbMath0934.20025OpenAlexW2092366824MaRDI QIDQ1283575

Franz G. Timmesfeld

Publication date: 2 February 2000

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/aima.1998.1779

zbMATH Keywords

sporadic groupsquadratic elementsquadratic pairsirreducible actionscentral productsquasisimple groupsfinite Lie-type groupsgeneral root subgroups

Mathematics Subject Classification ID

Simple groups (20E32) Buildings and the geometry of diagrams (51E24) Finite simple groups and their classification (20D05) Groups with a (BN)-pair; buildings (20E42)

Related Items (29)

Quadratic pairs. ⋮ Geometry of root elements in groups of type $\mathrm E_{6}$ ⋮ Algebraic structures related to universal covers of special rank one groups. ⋮ On the description of overgroups of \(E(m,R)\otimes E(n,R)\). ⋮ Cubic Action of a Rank one Group ⋮ Overgroups of elementary symplectic groups ⋮ Overgroups of $\mathrm{EO}(n,R)$ ⋮ LINEAR GROUPS OVER LOCALLY FINITE EXTENSIONS OF INFINITE FIELDS ⋮ Subgroups of Chevalley groups of types $B_l$ and $C_l$ containing the group over a subring, and corresponding carpets ⋮ Quadratic pairs without commuting root-subgroups. ⋮ Lie algebras generated by extremal elements. ⋮ Irreducible linear groups of degree four over a quaternion division algebra that contain a subgroup \(\text{diag}(T_3(K,\Phi_0),1)\). ⋮ Complete reducibility of quadratic modules for finite Lie-type groups. ⋮ Geometry of 1-tori in $\mathrm {GL}_n$ ⋮ Baumann-components of finite groups of characteristic \(p\), general theory ⋮ Some Completely Reducible Linear Groups over a Quaternion Division Ring Containing a Root Subgroup ⋮ On Linear Groups of Degree 2 Over a Noncommutative Division Algebra ⋮ Subgroups isomorphic to \(G_2(L)\) in orthogonal groups ⋮ Irreducible Linear Groups of Degree Four over a Quaternion Division Algebra that Contain a Root Subgroup ⋮ On Linear Groups of Degree 2nContaining a Representation of the Special Linear Group of Degreen ⋮ Overgroups of $E(m,R)⊗E(n,R)$ I. Levels and normalizers ⋮ Subgroups of rank one groups ⋮ Changes to a theorem of Timmesfeld. I: Quadratic actions. ⋮ Subgroups of symplectic groups that contain a subsystem subgroup. ⋮ Completely Reducible Linear Groups Over a Quaternion Division Algebra that Contain a Root Subgroup ⋮ Groups of Lie type generated by long root elements in \(F_4(K)\). ⋮ An equivariant analogue of Glauberman's \(ZJ\)-theorem ⋮ Cross characteristic representations of symplectic and unitary groups ⋮ Quadratic pairs without components

Cites Work

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